All Questions

Thinking of Cat as a mere 1-category, there is a 1-monad $\Lambda$ for the free cartesian closed category on a category. To every category X it assigns the category $\Lambda(X)$ whose objects are ...

I think this question Compact Hausdorff and C^*-algebra "objects" in a category. shows that there is no reciprocity between categories of algebra-objects of two algebraic categories. So, ...

TL;DR. Many cohomologies can be unified using comonads. Question: which cohomologies cannot be? For each algebraic theory, there is an adjunction, and therefore a (co)monad (or called a (co)triple). ...